Pemrograman Seni Fraktal

Ini adalah buku tentang desain fraktal yang sudah tidak lagi dicetak. Salah satu penulisnya adalah Profesor Pan Jingui, penerjemah "Pengantar Algoritma" versi China dan pembimbing doktoral di Departemen Ilmu Komputer di Universitas Nanjing.

Daftar isi
§1.1 Asal usul fraktal............................................ ..... ................................................. .......... ........................1
1.1.1 Fenomena fraktal biasa terjadi............................................ ... ................................................. ............ ........1
1.1.2 Asal usul "fraktal"................................ ......... ................................................. ...... ............2
1.1.3 Asal usul "fraktal"...................................... ... ................................................. ............ ............5
1.1.4 Hubungan antara fraktal dan matematika................................................ . ................................................. ............. .....9
1.1.5 Contoh fraktal................................................ ... ................................................... .................. ............10
§1.2 Kronik Fraktal............................................ ...... ................................................. ......... ........................ dua puluh satu
§1.3 Konsep fraktal............................................ .................................................. ................. ........................31
1.3.1 Pengertian fraktal............................................ .... ................................................. .......... .............31
1.3.2 Fraktal sebagai metode kognitif................................ .......... ................................................. ..... 35
1.3.3 Fraktal sebagai alat interpretasi............................................ ... ................................................37
§1.4 Dimensi fraktal............................................ ...... ................................................. ......... ................................42
1.4.1 Dari dimensi topologi ke dimensi metrik...................... ................... ................................................ .... 42
1.4.2 Pengukuran dimensi kesamaan diri...................................... .... ................................................. .......... .......47
1.4.3 Ukuran dimensi Hausdoff...................................... ...... ................................................. ......... ....49
1.4.4 Pengukuran dimensi kotak............................................ .... ................................................. .......................51
§1.5 Filsafat Fraktal.................................................. .................................................. ..................................................54
1.5.1 Fenomena fraktal di alam............................................ ... ................................................54
1.5.2 Fenomena fraktal dan filsafat generatif............................................ .. ...................................................56
§2.1 Arti seni............................................ .... ................................................. .......... .............59
2.1.1 Arti seni............................................ ... ................................................. ............ .............59
2.1.2 Pandangan yang mengingkari seni komputer................................ .......... ...................................61
2.1.3 Sanggahan terhadap pandangan negatif............................................ ... ................................................. ............ ...64
§2.2 Fraktal sebagai seni............................................ ..... ................................................. .......... ............69
2.2.1 Apa itu seni grafis fraktal...................................... .... ............................................69
2.2.2 Ciri-ciri seni fraktal................................ ........... ................................................. .... ......73
§2.3 Seni fraktal di Tiongkok............................................ .... ................................................. .......................79
§2.4 Cara menghasilkan seni fraktal............................................ ... ................................................. ............ .......83
2.4.1 Cara menghasilkan grafik fraktal................................ .......... ................................83
2.4.2 Metode keluaran dan tampilan grafik fraktal................................ ........ .................................85
§2.5 Prospek pengembangan seni fraktal................................ .......... ................................................. ..... .......86
2.5.1 Prospek pengembangan grafik fraktal................................ ......... ................................................86
2.5.2 Seni grafis dan dekoratif berukuran besar................................ .......... ................................87
2.5.3 Seni fraktal dan geometri baru...................................... .... ................................................. ............ 89
§3.1 Koordinat komputer................................................ .................................................. ..............................93
3.1.1 Komputer dapat melakukan lebih dari sekedar menghitung........................................ ..... ........................................ ............... ..94
3.1.2 Sistem operasi dan file................................................ ... ................................................. ............ ......95
3.1.3 Koordinat layar komputer............................................ .... ................................................. .......... ...101
§3.2 Format file warna dan gambar............................................ ... ................................................. ............ .........103
3.2.1 Sistem warna Munsell dan lain-lain............................................ .. ...................................................103
3.2.2 Nilai warna dan RGB............................................ ... ................................................. ............ .......106
3.2.3 Film pemisahan warna CMYK................................................ ..... ................................................. .......... .........109
3.2.4 Format file grafis............................................ .... ................................................. .......... ....110
§3.3 Inisialisasi grafis................................................ .................................................. ..............................114
§3.4 Fungsi grafik fraktal rekursif............................................ .... ................................................. .......... ........121
3.4.1 Kurva pusaran................................................ ..... ................................................. .......... ............121
3.4.2: Kurva Koch............................................ .... ................................................. ............ ............122
§3.5 Menghasilkan grafik meta-fraktal............................................ ... ................................................. ............ .......123
3.5.1 Setiap ruas garis generator mempunyai panjang yang sama.................................. ... ................................................... ..123
3.5.2 Panjang setiap ruas garis generator berbeda-beda................................ ... .................130
3.5.3 Panjang dan arah putaran setiap ruas garis generator berbeda-beda................................. ............137
§3.6 Grafik fraktal pemetaan titik tetap................................... ... ................................................. ..............138
§3.7 Pola gambar grafis fraktal...................................... ...... ................................................. ......... ........144
§4.1 Set tiga titik penyanyi...................................... ..... ................................................. .......... ............149
§4.2 Kurva Peano dan Kurva Hilbert............................................ ... ................................................. ............ .153
§4.3 Kurva Koch............................................ .................................................. ..............................160
§4.4 Karpet Sierpinski................................................ .................................................. ................. ............163
§4.5 Durer Pentagon................................................ .................................................. ..............................174
§5.1 Kurva pohon........................................ ...... ................................................. ......... ............177
§5.2 Grafik dengan segmen garis sebagai elemen penyusunnya...................................... ... ................................................180
§5.3 Grafik dengan lingkaran sebagai elemen penyusunnya...................................... .... ................................................. .......... ...184
§5.4 Grafik dengan poligon sebagai elemen penyusunnya............................................ .. ...................................................190
§5.5 Grafik dengan bintang sebagai elemen penyusunnya............................................ .. ................................................. ............ 193
§6.1 Sistem Lin............................................ .................................................. ................. ........................199
§6.2 Contoh dan kodesemu................................................ ..... ................................................. .......... ............201
§6.3 L tabel data sistem................................................ ................................................ ............... .............209
§6.4 Sistem fungsi berulang...................................... ....... ................................................. ........ ............216
§6.5 Model aglomerasi terbatas difusi................................ ........... ................................................. .............232
§7.1 Operasi bilangan kompleks dan iterasi barisan titik................................ ......... ................................................. ...... ......237
7.1.1 Empat operasi aritmatika pada bilangan kompleks............................................ . ................................................. ............. .......237
7.1.2 Urutan titik pada bidang kompleks............................................ . ................................................. ....................244
7.1.3 Perubahan tak terduga................................................ ..... ................................................. .......... .....247
§7.2 Koleksi Julia............................................ .................................................. ..................................................251
§7.3 Himpunan Mandelbrot............................................ .................................................. ................. ............263
§7.4 Julia mengatur dekripsi................................................ ... ................................................... ................. ............271
§7.5 Situasi berdimensi tinggi dan tingkat tinggi...................................... .. ................................................. ............. .............279
7.5.1 Kasing berdimensi tinggi...................................... ..... ................................................. .......... ............279
7.5.2 Situasi tingkat tinggi................................ ............ ................................................. ...............281
7.5.3 Himpunan Mandelbrot yang digeneralisasikan dan himpunan Julia................................ ......... ................................................282
§7.6 Metode Newton untuk mencari akar............................................ ... ................................................. ............ .............287
§7.7 Klasifikasi wilayah yang berbeda............................................ .... ................................................. .......................294
§8.1 Peta logistik satu dimensi...................................... ..... ................................................. .......... .......301
§8.2 Indeks Lyapunov............................................ ...... ................................................. ......... ............307
§8.3 Peta Kekacauan Ganda................................................ ... ................................................... ................. .............309
§8.4 Pemetaan standar................................................ .................................................. ..............................318
§8.5 Pemetaan wilayah Ainongbao................................................ ..... ................................................. .......... ............324
§8.6 Pemetaan raja............................................ .................................................. ..............................327
§8.7 Pemetaan Elang Bersayap Tiga............................................ ... ................................................. ............ .............334
§9.1 Cara mendapatkan perangkat lunak...................................... ..... ................................................. .......... ............338